The lambda norm of a \(K\) -type \(\mu \)  was introduced by Vogan [1]}. Choose an index \(0\le j\le 62\)  such that \(\mu +2\rho _c\in \mathcal {C}^{(j)}\) .
Put
\(\lambda _a(\mu ):=P(\mu +2 \rho _c -\rho ^{(j)}).\) 
